Three liquids have the same surface tension and densities $\varrho_{1}, \varrho_{2}$,and $\varrho_{3}$ $(\varrho_{1} > \varrho_{2} > \varrho_{3})$. In three identical capillaries,the rise of liquid is the same. The corresponding angles of contact $\theta_{1}, \theta_{2}$,and $\theta_{3}$ are related as:

Two capillaries made of the same material have radii $r_1 = 1 \, mm$ and $r_2 = 2 \, mm$. If the rise of the liquid in the first capillary $(r_1 = 1 \, mm)$ is $30 \, cm$,then the rise in the other capillary will be ........ $cm$.

Two tubes of same length and diameters $4 \ mm$ and $8 \ mm$ are joined together to form a $U$-shaped tube open at both the ends. If the $U$-tube contains water,then the difference between the levels of water in the two limbs of the tube is (Surface tension of water at the temperature of experiment is $7.3 \times 10^{-2} \ N \ m^{-1}$,angle of contact $= 0^{\circ}$,density of water $= 1.0 \times 10^3 \ kg \ m^{-3}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $mm$)

Water rises in a capillary tube up to a height $h$. If this capillary tube is tilted by an angle of $45^o$,then the length of the water column in the capillary tube becomes

Two capillaries of the same material but of different radii are dipped in a liquid. In one of the capillaries,the liquid rises to a height of $22 \ cm$ and in the other to $66 \ cm$. The ratio of their radii is

If the diameter of a capillary tube is doubled,then the height of the liquid that will rise is